The deep borehole heat exchanger (DBHE) shows great potential in seasonal thermal energy storage and its high performance efficiency with smaller land occupancy attracts increasing attention as a promising geothermal energy exploitation technique. With respect to a vertical BHE with extremely long length pipes buried underground, thermal analysis of the unsteady heat transfer process of the system is quite complicated. Due to the high temperature underground, the deeper part of BHE can extract more heat from the rock, which leads to a higher heat extraction rate. The heterogeneous distribution of heat flux density and geothermal gradient cannot be described properly by the existing analytical models. Although a full 3D numerical solution can reflect these features, it always requires high computational resources and presents numerical instabilities. In this paper, we propose a hybrid modeling method with high efficiency to simulate the temperature evolution inside the DBHE, and the heat propagation front in the surrounding rock mass. The temperature evolution inside the DBHE is solved by finite difference schemes, while the heat propagation in the surrounding rock is determined by an analytical formulation of thermal impacted radius. The coupling is achieved via source/sink term by incorporating the heat flux between the DBHE and the surrounding rock. Furthermore, an innovative analytical formulation describing the heat flux density is also presented, which accounts for the key parameters affecting the thermal performance of the DBHE system. Our proposed model is further verified against results with full 3D numerical solution under the same configurations. It is demonstrated that the proposed model can capture the key physical process of the heat transfer problem, while maintaining the calculation accuracy required by the engineering application. Regarding the calculation speed, the model results are around 30 times faster when compared to the full 3D numerical solution.

中文翻译：

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用于深井换热器热分析的有效混合模型

深孔换热器（DBHE）在季节性热能存储方面显示出巨大潜力，其高效能和较小的土地占用率已成为一种有前途的地热能开发技术，受到越来越多的关注。对于具有埋在地下的超长管道的垂直BHE，对系统不稳定传热过程的热分析非常复杂。由于地下高温，BHE的较深部分可以从岩石中提取更多的热量，从而导致更高的热量提取率。现有分析模型无法正确描述热通量密度和地热梯度的异质分布。尽管完整的3D数值解决方案可以反映这些功能，它总是需要大量的计算资源，并且存在数值不稳定性。在本文中，我们提出了一种高效的混合建模方法，以模拟DBHE内部的温度演化以及周围岩体中的热传播前沿。DBHE内部的温度演化通过有限差分方案解决，而围岩中的热传播则通过热影响半径的解析公式确定。通过合并DBHE与周围岩石之间的热通量，可以通过源/汇项实现耦合。此外，还提出了描述热通量密度的创新分析公式，该公式解释了影响DBHE系统热性能的关键参数。在相同的配置下，我们提出的模型可通过完整的3D数值解决方案针对结果进行验证。结果表明，所提出的模型可以捕获传热问题的关键物理过程，同时保持工程应用所需的计算精度。关于计算速度，与完整的3D数值解决方案相比，模型结果要快30倍左右。